Question Number 151080 by malwan last updated on 18/Aug/21 $${if}\:\left({f}\circ{f}\circ{f}\circ{f}\right)\left({x}\right)=\mathrm{16}{x}+\mathrm{15} \\ $$$${find}\:{f}\left({x}\right) \\ $$ Answered by Mokmokhi last updated on 18/Aug/21 $$\mathrm{It}\:\mathrm{is}\:\mathrm{reasonable}\:\mathrm{to}\:\mathrm{say}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{linear}\:\mathrm{by}\:\mathrm{rejecting}\:\mathrm{other}\:\mathrm{possibilities}. \\ $$$$\mathrm{Then}\:{f}\left({x}\right)={ax}+{b}\:\mathrm{for}\:\mathrm{some}\:\mathrm{unknowns}\:{a}\:\mathrm{and}\:{b}. \\…
Question Number 151082 by mathdanisur last updated on 18/Aug/21 Commented by Mokmokhi last updated on 18/Aug/21 $$\mathrm{This}\:\mathrm{can}\:\mathrm{be}\:\mathrm{proven}\:\mathrm{starting}\:\mathrm{from}\:\mathrm{left}. \\ $$$$\mathrm{By}\:\mathrm{substituting}\:{u}=\frac{\pi}{\mathrm{2}}−{x}. \\ $$$$\mathrm{After}\:\mathrm{evaluation}.\:\mathrm{By}\:\mathrm{dummy}\:\mathrm{variables}\:\mathrm{done}. \\ $$ Terms of…
Question Number 85542 by TawaTawa1 last updated on 22/Mar/20 Commented by TawaTawa1 last updated on 22/Mar/20 $$\mathrm{Evaluate}:\:\:\:\:\:\underset{{x}\rightarrow\frac{\mathrm{x}}{\mathrm{2}}} {\mathrm{lim}}\:\:\left(\mathrm{x}\:\:−\:\:\frac{\pi}{\mathrm{2}}\right)\:\mathrm{tan}\:\mathrm{x} \\ $$ Commented by mathmax by abdo…
Question Number 151079 by mathdanisur last updated on 18/Aug/21 Answered by dumitrel last updated on 18/Aug/21 Commented by dumitrel last updated on 18/Aug/21 Commented by…
Question Number 85540 by M±th+et£s last updated on 22/Mar/20 $${find}\:{the}\:{range} \\ $$$${y}=\frac{{x}+\left[{x}\right]}{\mathrm{1}−\left[{x}\right]+{x}} \\ $$ Answered by mr W last updated on 23/Mar/20 $${for}\:{x}\geqslant\mathrm{0}: \\ $$$${let}\:{x}={n}+{d}\:{with}\:\mathrm{0}\leqslant{d}<\mathrm{1}…
Question Number 151078 by mathdanisur last updated on 18/Aug/21 $$\Omega_{\boldsymbol{\mathrm{k}}} =\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\:\centerdot\underset{\boldsymbol{\mathrm{p}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\frac{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{p}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{n}+\mathrm{k}}\\{\mathrm{n}+\mathrm{p}}\end{pmatrix}}\:\:;\:\:\mathrm{k}\in\mathbb{N}^{\ast} -\mathrm{fixed} \\ $$$$\mathrm{find}\:\:\Omega=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\Omega_{\boldsymbol{\mathrm{n}}-\mathrm{1}} }\:\centerdot\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\sqrt[{\boldsymbol{\mathrm{i}}^{\mathrm{2}} }]{\boldsymbol{\mathrm{i}}!}\: \\ $$ Terms…
Question Number 151073 by mathdanisur last updated on 18/Aug/21 $$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\begin{pmatrix}{\mathrm{50}}\\{\mathrm{0}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{1}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{2}}\end{pmatrix}^{\mathrm{2}} +…+\begin{pmatrix}{\mathrm{50}}\\{\mathrm{49}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{50}}\end{pmatrix}^{\mathrm{2}} \\ $$ Answered by ArielVyny last updated on 18/Aug/21…
Question Number 20001 by Tinkutara last updated on 20/Aug/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic} \\ $$$$\mathrm{equation}\:\mathrm{8sec}^{\mathrm{2}} \theta\:−\:\mathrm{6sec}\theta\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 20/Aug/17 $$\mathrm{8sec}^{\mathrm{2}} \theta\:−\:\mathrm{6sec}\theta\:+\:\mathrm{1}\:=\:\mathrm{0} \\…
Question Number 151074 by sarahg1186 last updated on 18/Aug/21 $$\mathrm{5}+\mathrm{5}+\mathrm{5} \\ $$ Answered by sarahg1186 last updated on 18/Aug/21 $$\mathrm{15} \\ $$ Terms of Service…
Question Number 151069 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left(\mathrm{1145141919810893x}\right)}{\mathrm{x}\left(\mathrm{cosh}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)}\mathrm{dx}=\frac{\pi}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com